Abstract
The aim of this work is to discuss the behavior of quantum fields at finite temperature. Initially, we will introduce phenomenologically the basic relativistic, quantum and thermal elements (Planck-Einstein), by describing the behavior of radiation in equilibrium with a cavity, the celebrated black body problem. Then, we will show that a proper language for describing this physical phenomena is the language of non-massive scalar fields (Klein-Gordon-Fock) in (3 + 1) dimensions, at thermal equilibrium. For this purpose, we will study the problem in the formalism of operators and a posteriori in the formalism of functional integration, by considering the density matrix of states. In addition, we will approach the problem in different representations (coordinates/momentum). The connection between a quantum theory in Minkowski space-time and a quantum theory in thermal equilibrium in Euclidean space by means of a Wick rotation (imaginary time) will be implemented by means of the appropriate similarity transformations.
Keywords:
Classical Field Theory; Quantum Field Theory; Thermal Quantum Fields Theory